According to 0 A.D., their soundtrack is available under the Creative Commons Attribution-ShareAlike (CC BY-SA) 3.0 license which allows me to redistribute their songs without asking their permission, as long as I give them credit and distribute the songs under the same license or a similar free license.
See here: https://play0ad.com/media/music/

Can I also do this with Wesnoth's music? And can I convert the songs from .ogg to .mp3? Because Morrowind's game engine will not read .ogg music files.

Please don't consider this an official answer, but if I am reading and interpreting it correctly, it means you are free to distribute all the official music in current versions of Wesnoth according to the terms of the CC BY-SA 4.0 license. Our community manager Vultraz may be able to provide more clarity on that point.

I have already private messaged community manager Vultraz, I haven't received a reply.

Based off my understanding of the GNU General Public License v2.0, I am allowed to distribute and modify the songs, in this case, I am modifying the songs, converting ogg to mp3, and the converting software I am using is Audacity.